Eigenstate Definition and 88 Threads

Hey guys, So this question is sort of a fundamental one but I'm a bit confused for some reason. Basically, say I have a Hermitian operator \hat{A}. If I have a system that is prepared in an eigenstate of \hat{A}, that basically means that \hat{A}\psi = \lambda \psi, where \lambda is real...

Homework Statement Hey guys! So this is a bit of a long question, I've done most of it but I need a few tips to finish the last part, and I'm not sure if I've done the first one correctly. I'll be typing it up in Word cos Latex is long! http://imageshack.com/a/img5/8335/n7iw.jpg...

Eigenstates of some observable O are represented by orthonormal vectors in complex Hilbert space. Is it true that the only possible way that the state vector can evolve from one eigenstate of O to the next, is to rotate between the two eigenvectors so that intermediate state vectors are...

Eigenvectors associated with distinct values of an observable are orthogonal, according to quantum mechanics. Does this entail that a quantum system cannot continuously evolve from one eigenstate into another, for ANY observable? At first, that seems strange: it seems like a particle...

Homework Statement Hi. I'm looking at a hydrogen atom, which normalized stationary states is defined as |nlm> The hydrogen atom is described by the normalized wavefunction: \left| \psi \right\rangle =\frac{1}{\sqrt{2}}\left( \left| 210 \right\rangle +\left| 211 \right\rangle \right)...

Hi PF members, I am stuck with a problem about larmor precession. I cannot find the eigenstates of the hamiltonian given as H = \frac{\hbar}{2}\begin{pmatrix} \omega_{0} & \omega_{1}\delta(t-t') \\ \omega_{1}\delta(t-t') & \omega_{0} \end{pmatrix} Can anyone help me? Since it has time...

I started a new thread from a side discussion in https://www.physicsforums.com/showthread.php?t=681625&page=2, since it seems very off topic, but I still had questions. Is there a requirement for an operator that corresponds to an observable to be part of a complete set, ie. its...

Hi all, This may seem silly but...do energy eigenstates always exist in terms of wave functions themselves? To me, it seems they do because they always contain quantized energies. How about any hypothetical non-normalizeable wave functions? Thanks O.

Homework Statement A 3D harmonic oscillator has the following potential: V(x,y,z) = \frac{1}{2}m( \varpi_{x}^2x^2 + \varpi_{y}^2y^2 + \varpi_{z}^2z^2) Find the energy eigenstates and energy eigenvalues for this system. The Attempt at a Solution I found the energy eigenvalue to...

show that e-ikx is an eigenstate energy. Do I start by multiplying the hamiltonian operator by ψ(x)? So far I have ψ(x)(1/2m)(-ihd/dx)2=e-ikx

Hi all, just studying for my final exam and needed a little clarification on this. Our prof did an example: Consider a particle of mass m moving in the nth energy eigenstate of a one-dimensional infinite square well of width L. What is the uncertainty in the particle's energy? He said the...

Homework Statement Explain what happens when a particle transitions from the 3rd eigenstate to the second eigenstate. If the total energy in the 3rd eigenstate is 2.47x10^19J and the energy in the 2nd eigenstate is 1.1x10^-19J calculate the energy released and the wavelength of the emitted...

2 questions on symmetries: "conserved in interaction => eigenstate in interaction"? Hello, I'm currently taking an introductory course in elementary particles (level: Griffiths) and I have 2 questions that are severely bothering me; all help is appreciated! They are related to Griffiths'...

Homework Statement The square angular momentum L2 and the z-component Lz of a free particle are measured. They are found to be L2=6\hbar^2 and Lz=\hbar What is the state |l,m> of the system after measurement? Homework Equations L2|l,m>=\hbar^2l|l,m> Lz|l,m>=\hbarm|l,m> The...

Homework Statement Find [Lz, Px] and [Lz,Py] and use this to show that \langle l'm'|P_x|lm\rangle = 0 for m' \neq m \pm 1. Homework Equations L_z|lm\rangle = \hbar m |lm\rangle L^2|lm\rangle = \hbar^2 l(l+1)|lm\rangle L_{\pm}|lm\rangle = \hbar \sqrt{l(l+1)-m(m\pm 1)}|l,m\pm 1 \rangle...

Homework Statement A free particle (de Broglie wave) may be represented by the wave-function \psi(x)=Aeikx Show that this is an eigenstate of the momentum operator \hat{p}=-\hbar\frac{\delta}{\deltax}Homework Equations \hat{p}un(x)=anun(x) an is the eigenvalue un(x) is the corresponding...

Hi, We know that when we have one flavour of neutrino, it can change into another flavour by neutrino oscillations. However, if we consider a mass eigenstate, then is it true that it can never change into a different mass eigenstate? In other words is a |v_{1}> neutrino forever a |v_{1}>? I...

Homework Statement The Hamiltonian of a quantum-mechanical system has only two energy eigenstates, namely |1> and |2>. The system has three other properties, denoted by the observables A, B, and C, respectively. The normalized eigenstates |1> and |2> may or may not be eigenstates of A, B, or...

Homework Statement I am trying to translate what is meant by: <psi | p | psi> <psi|p^2|psi> <psi | x | psi> In a mathematicaly context as shown by this link: http://answers.yahoo.com/question/index?qid=20110521103632AASz9Hm Can anyone specify what these mean? Thanks!

Homework Statement An atomic system has 2 alternative 2-state bases. The angular momentum bases are \left | \mu_i \right \rangle with L_0 = 0 and L_1 = 1. The energy eigenstates are \left | \phi_i \right \rangle with E_0 and E_1. All states are normalised and: \left | \mu_0 \right...

Homework Statement Hi; I am trying to construct eigenstate for the given hamiltonian. I have the energy eigenvalues and corresponding eigenvectors. But How can I construct eigenstates? Homework Equations The Attempt at a Solution I tried to use the H . Psi= E . Psi...

Homework Statement In quantum mechanics a physical observable is represented by an operator A. Define the terms eigenstate, eigenvalue and eigenfunction of a quantum mechanical operator. Homework Equations The Attempt at a Solution I think I know in that eq 'f' is the eigenfunction, and...

can the neutrino mass eigenstate couple to the group of SU(2) doublet?if we intentionally not impose any flavor symmetry on it. \left(\begin{array}{c}\nu_{1}\\e\end{array}\right)

can anybody explain what is the difference between neutrino flavour state and neutrino mass eigenstate?getting confuse on it again...

Homework Statement I'm really struggling with this one guys, the question is: Explain why a particle which is in an energy eigenstate cannot be moving in the classical sense. Homework Equations I'm guessing the TISE and TDSE are relevant The Attempt at a Solution

I'm really struggling with this one guys, the question is: Explain why a particle which is in an energy eigenstate cannot be moving in the classical sense.

Homework Statement The system described by the Hamiltonian H_0 has just two orthogonal energy eigenstates, |1> and |2> , with <1|1>=1 , <1|2> =0 and <2|2>=1 . The two eignestates have the same eigenvalue , E_0: H_0|i>=E_0|i>, for i=1 and 2. Now suppose the Hamiltonian for the...

Show that wave packet is an eigenstate to operator [SOLVED] Homework Statement For a harmonic oscillator we can define the step up and down operators \hat{a} and \hat{a}^{\dagger} and their action as \hat{a}=\sqrt{\frac{m\omega}{2\hbar}}(\hat{x}+\frac{\imath}{m\omega}\hat{p}) \quad...

The spin-orbit interaction in Hydrogen adds an extra term \alpha \mathbf{L} \cdot \mathbf{S} to the Hamiltonian of the system. If the electron is in an energy eigenstat show that it cannot also be in an eigenstate of either L_z or S_z. I have that the modified Hamiltonian is given as...

Hi, I've got a problem that is to calculate the normalisation constant and then the probability of obtaining an energy measurement of E_n for an infinite square well. I often find out that I have made a mistake along the way which has made the problem ten times more complicated than it...

what the differ between eigenstate and eigenfunction ?

Suppose we prepare a system in some properly normalized superposition of the spherical harmonics: A|11> + B|10> + C|1-1>. One of the fundamental results of quantum mechanics is that, if we measure L_z, we will collapse the state of the system onto an eigenstate of the eigenvalue we measure. My...

Homework Statement Obtain an expression for the expectation value <Pxn>n N=1,2... of a particle in an infinite box ( V=\infty for x<0 and x>L ; V=0 for 0<X<L) which is in an eigenstate of the energy. Homework Equations Pn =+- \sqrt{2*m*En } = +- (n*pi*Hbar) / L The Attempt at a...

Hi I use liboff quantum mechanics textbook fourth edition. 5.25 fomula of 122 page is \frac{1}{\sqrt{2\pi}}e^{ikx} I thought it is nomalized, but i don't know exactly why \sqrt{2\pi} is denominator. I think it seemed to be linked Dirac-delta function [itex]...

Hi, I have a question about the momentum eigenstates in a 1D infinite square well example. First of all, are there any eigenstates at all in this example? By explicitly applying the wavefunction(stationary states) which can be easily obtained from the boundary conditions, it can shown that the...

Let's consider the hydrogen atom with one electron. If we observe the energy the result is always one of the eigenvalues even if the statefunction is arbitrary. I accept that. But why is the atom always treated as if the electron is in one of the eigenstates? Why is the statefunction always...

I'm a little bit confused in general about what an eigenstate is. So say we have something like: H|n>=hw(N+1/2)|n> |n> is the eigenket, hw(N+1/2) is the eigenvalue, but what exactly is an eigenstate? The entire question asks if there are eigenstate to the creation operator and to prove it...

Trying to get my head around this problem and would very much appreciate any suggestions. Given a wavefunction \psi(X) i am asked if it is an energy eigenstate for a free particle moving in one dimension? Any suggestion on how I start a problem like this? thanks, Epud